Problem $4\mathrm{.}6$

A $3500$ lb cannon fires a cannonball. Just after firing, the cannon moves backward at $-9f\frac{t}{s}.$ The recoil

mechanism consists of two pads and a beam. Assume the pads are located close enough to the beam's

center that you can model them as acting at the center.

a$)$ Find the response of the cannon after it has fired. GO THROUGH THE STEPS!

b$)$ Plot the response of the cannon. How long does it take the cannon to stay within $0\mathrm{.}2$ in of its

original position?

Answer: a$)x(t)=3\mathrm{.}42e^{-27\mathrm{.}6t}sin(31\mathrm{.}6t+)$ in